OK, let's crack this. We're given 623 and our task is to multiply it by 38. Essentially, we'll be adding 623 to itself 38 times.
Step 1: 0 + 623 = 623
Step 2: 623 + 623 = 1246
Step 3: 1246 + 623 = 1869
Step 4: 1869 + 623 = 2492
Step 5: 2492 + 623 = 3115
Step 6: 3115 + 623 = 3738
Step 7: 3738 + 623 = 4361
Step 8: 4361 + 623 = 4984
Step 9: 4984 + 623 = 5607
Step 10: 5607 + 623 = 6230
Step 11: 6230 + 623 = 6853
Step 12: 6853 + 623 = 7476
Step 13: 7476 + 623 = 8099
Step 14: 8099 + 623 = 8722
Step 15: 8722 + 623 = 9345
Step 16: 9345 + 623 = 9968
Step 17: 9968 + 623 = 10591
Step 18: 10591 + 623 = 11214
Step 19: 11214 + 623 = 11837
Step 20: 11837 + 623 = 12460
Step 21: 12460 + 623 = 13083
Step 22: 13083 + 623 = 13706
Step 23: 13706 + 623 = 14329
Step 24: 14329 + 623 = 14952
Step 25: 14952 + 623 = 15575
Step 26: 15575 + 623 = 16198
Step 27: 16198 + 623 = 16821
Step 28: 16821 + 623 = 17444
Step 29: 17444 + 623 = 18067
Step 30: 18067 + 623 = 18690
Step 31: 18690 + 623 = 19313
Step 32: 19313 + 623 = 19936
Step 33: 19936 + 623 = 20559
Step 34: 20559 + 623 = 21182
Step 35: 21182 + 623 = 21805
Step 36: 21805 + 623 = 22428
Step 37: 22428 + 623 = 23051
Step 38: 23051 + 623 = 23674

So, 623*38 = 23674